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This study investigated the irreversible energy losses in the different sections of propeller blades. To the best of our knowledge, this is the first study to consider the properties of a shear-thinning fluid in evaluating irreversible energy losses based on the entropy generation theory. The numerical simulation results were consistent with the experimental results. The flow energy losses and the total mechanical energy loss gradient of an anaerobic digestion (AD) system were determined. The results indicated that the total mechanical energy loss occurred in the propeller region and was primarily influenced by the operation speed. The effects of rheology were neglected, although rheology notably affects the equivalent-volume velocity field within specific power characteristics, leading to an insufficient mixing field in the AD system. The energy losses primarily occurred around the propeller region, primarily in sections 3–5 under different flow rates. Viscous diffusion and velocity fluctuation are the primary factors contributing to the entropy of the system, accounting for more than 98%. According to the wall separation and friction loss on the suction and pressure surfaces of the propellers, sections 3–5 accounted for 90% of the energy loss. Energy dissipation in the propeller was mostly constituted by turbulence entropy and direct entropy. The rotation speed was the key factor causing viscous diffusion. Although the rheology effect on hydraulic loss is limited at low concentrations, the hydraulic loss in the blade tip region due to high-concentration fluids is significantly affected by rheology.

Detailed power consumption characteristics from experiments and simulations of gas–liquid stirred tanks with shear-thinning power-law liquids are presented. The motion of bubbles was investigated based on the Euler–Euler approach with a bubble cluster concept. The drag coefficient of bubbles with a constant bubble diameter was modeled as the Schiller and Naumann function. The predicted power consumption of a gas–liquid mixture shows reasonable agreement with experimental data with a maximum deviation of 8.9%. For the studied aerated systems, a qualitatively new power reduction correction equation was derived and demonstrated a reasonable agreement with experimental results compared with the literature-reported equations. The effect of the concentrations and gas flow rates on power consumption was presented. It was found that the power consumption of different mixtures is related to the change in the critical generalized Reynolds number, which was Reg = 440, 230, 100, 30, and 25 for 0.2%, 0.4%, 0.62%, 0.85%, and 1.25%, respectively.